A New Model for Metaballs

The research for my MSc in Computer Science was on the mathematics and geometry of metaballs. It was an intersting topic that let me combine my interests in Chemistry, Mathematics and Computer Science.

An interesting problem in using metaballs is in controlling the blending between the balls. The blending concepts of metaballs originate from molecular bonding theories used in Chemistry. Since chemists have no problems in using these theories to create physical and computational models, I decided that adapting more ideas from chemistry could be used to solve blending problems in metaballs.

Adding Blending Control to Rayshade

The following two soft objects are based on the blob example object from the RayShade raytracing package. The image on the right is rendered with my new model and demonstrated how blending control can be used to generate a gap in a metaball.

A more extensive example

The following two images show how blending control can be used to create soft objects with internal boundries such as the fingers on a hand. The image on the left is generated using a standard metaball, while the image on the right is generated using blending control from my new model.

Bounding Volume Enhancements

Additional enhancements benefits to the rendering algorithminclude a smaller bounding box for the object, as seen in the image below. The red rectangle is a cross section of the bounding box of corresponding to the rendered object. The blue box is the corresponding cross section of the bounding box used by the new rendering algorithm.

Partial Geometric Surface-Solutions

Large portions of a metaball's surface can be computed using only the geometry of the key points rather than relying on the solution of a quartic root solving package. The image below shows the geometrically solved portions of in pink marble, while the black sections of the object require standard quartic root solving techniques.